arXiv subjects

Barbara Drossel

Publications and source records attributed to Barbara Drossel.

At least 91 records · Page 5Linked to original sources

arXiv2000

Spin glasses without time-reversal symmetry and the absence of a genuine structural glass transition

We study the three-spin model and the Ising spin glass in a field using Migdal-Kadanoff approximation. The flows of the couplings and fields indicate no phase transition, but they show even for the three-spin model a slow crossover to the asymptotic high-temperature behaviour for strong values of the couplings. We also evaluated a quantity that is a measure of the degree of non-self-averaging, and we found that it can become large for certain ranges of the parameters and the system sizes. For the spin glass in a field the maximum of non-self-averaging follows for given system size a line that resembles the de Almeida-Thouless line. We conclude that non-self-averaging found in Monte-Carlo simulations cannot be taken as evidence for the existence of a low-temperature phase with replica-symmetry breaking. Models similar to the three-spin model have been extensively discussed in order to provide a description of structural glasses. Their theory at mean-field level resembles the mode-coupling theory of real glasses. At that level the one-step replica symmetry approach breaking predicts two transitions, the first transition being dynamical and the second thermodynamical. Our results suggest that in real finite dimensional glasses there will be no genuine transitions at all, but that some features of mean-field theory could still provide some useful insights.

cond-mat.dis-nn↗

arXiv2000

The Influence of Predator-Prey Population Dynamics on the Long-term Evolution of Food Web Structure

We develop a set of equations to describe the population dynamics of many interacting species in food webs. Predator-prey interactions are non-linear, and are based on ratio-dependent functional responses. The equations account for competition for resources between members of the same species, and between members of different species. Predators divide their total hunting/foraging effort between the available prey species according to an evolutionarily stable strategy (ESS). The ESS foraging behaviour does not correspond to the predictions of optimal foraging theory. We use the population dynamics equations in simulations of the Webworld model of evolving ecosystems. New species are added to an existing food web due to speciation events, whilst species become extinct due to coevolution and competition. We study the dynamics of species-diversity in Webworld on a macro-evolutionary timescale. Coevolutionary interactions are strong enough to cause continuous overturn of species, in contrast to our previous Webworld simulations with simpler population dynamics. Although there are significant fluctuations in species diversity because of speciation and extinction, very large scale extinction avalanches appear to be absent from the dynamics, and we find no evidence for self-organised criticality.

nlin.AO↗

arXiv2000

The influence of critical behavior on the spin glass phase

We have argued in recent papers that Monte Carlo results for the equilibrium properties of the Edwards-Anderson spin glass in three dimensions, which had been interpreted earlier as providing evidence for replica symmetry breaking, can be explained quite simply within the droplet model once finite size effects and proximity to the critical point are taken into account. In this paper, we show that similar considerations are sufficient to explain the Monte Carlo data in four dimensions. In particular, we study the Parisi overlap and the link overlap for the four-dimensional Ising spin glass in the Migdal-Kadanoff approximation. Similar to what is seen in three dimensions, we find that temperatures well below those studied in Monte Carlo simulations have to be reached before the droplet model predictions become apparent. We also show that the double-peak structure of the link overlap distribution function is related to the difference between domain-wall excitations that cross the entire system and droplet excitations that are confined to a smaller region.

cond-mat.dis-nn↗

arXiv2000

Phase ordering and roughening on growing films

We study the interplay between surface roughening and phase separation during the growth of binary films. Already in 1+1 dimension, we find a variety of different scaling behaviors depending on how the two phenomena are coupled. In the most interesting case, related to the advection of a passive scalar in a velocity field, nontrivial scaling exponents are obtained in simulations.

cond-mat.stat-mech↗

arXiv1999

The Link Overlap and Finite Size Effects for the 3D Ising Spin Glass

We study the link overlap between two replicas of an Ising spin glass in three dimensions using the Migdal-Kadanoff approximation and scaling arguments based on the droplet picture. For moderate system sizes, the distribution of the link overlap shows the asymmetric shape and large sample-to-sample variations found in Monte Carlo simulations and usually attributed to replica symmetry breaking. However, the scaling of the width of the distribution, and the link overlap in the presence of a weak coupling between the two replicas are in agreement with the droplet picture. We also discuss why it is impossible to see the asymptotic droplet-like behaviour for moderate system sizes and temperatures not too far below the critical temperature.

cond-mat.dis-nn↗

arXiv1999

On the scaling behavior of the abelian sandpile model

The abelian sandpile model in two dimensions does not show the type of critical behavior familar from equilibrium systems. Rather, the properties of the stationary state follow from the condition that an avalanche started at a distance r from the system boundary has a probability proportional to 1/sqrt(r) to reach the boundary. As a consequence, the scaling behavior of the model can be obtained from evaluating dissipative avalanches alone, allowing not only to determine the values of all exponents, but showing also the breakdown of finite-size scaling.

cond-mat.dis-nn↗

arXiv1999

A simple model for the formation of a complex organism

A simple model for the formation of a complex organism is introduced. Individuals can communicate and specialize, leading to an increase in productivity. If there are limits to the capacity of individuals to communicate with other individuals, the individuals form groups that interact with each other, leading to a complex organism that has interacting units on all scales.

adap-org↗

arXiv1998

Comment on "General Method to Determine Replica Symmetry Breaking Transitions"

In a recent letter Marinari et al [Phys. Rev. Lett. 81, 1698 (1998)] introduced a new method to study spin glass transitions and argued that by probing replica symmetry (RS) as opposed to time reversal symmetry (TRS), their method unambiguously shows that replica symmetry breaking (RSB) occurs in short-range spin glasses. In this comment we show that while the new method is indeed useful for studying transitions in systems where TRS is absent (such as the p-spin model studied by them), the conclusion that it shows the existence of RSB in short-range spin glasses is wrong.

cond-mat.dis-nn↗

arXiv1998

Evidence for the droplet/scaling picture of spin glasses

We have studied the Parisi overlap distribution for the three dimensional Ising spin glass in the Migdal-Kadanoff approximation. For temperatures T around 0.7Tc and system sizes upto L=32, we found a P(q) as expected for the full Parisi replica symmetry breaking, just as was also observed in recent Monte Carlo simulations on a cubic lattice. However, for lower temperatures our data agree with predictions from the droplet or scaling picture. The failure to see droplet model behaviour in Monte Carlo simulations is due to the fact that all existing simulations have been done at temperatures too close to the transition temperature so that sytem sizes larger than the correlation length have not been achieved.

cond-mat.dis-nn↗

arXiv1998

Extinction events and species lifetimes in a simple ecological model

A model for large-scale evolution recently introduced by Amaral and Meyer is studied analytically and numerically. Species are located at different trophic levels and become extinct if their prey becomes extinct. It is proved that this model is self-organized critical in the thermodynamic limit, with an exponent 2 characterizing the size distribution of extinction events. The lifetime distribution of species, cutoffs due to finite-size effects, and other quantities are evaluated. The relevance of this model to biological evolution is critically assessed.

adap-org↗

arXiv1998

Depinning of a domain wall in the 2d random-field Ising model

We report studies of the behaviour of a single driven domain wall in the 2-dimensional non-equilibrium zero temperature random-field Ising model, closely above the depinning threshold. It is found that even for very weak disorder, the domain wall moves through the system in percolative fashion. At depinning, the fraction of spins that are flipped by the proceeding avalanche vanishes with the same exponent beta=5/36 as the infinite percolation cluster in percolation theory. With decreasing disorder strength, however, the size of the critical region decreases. Our numerical simulation data appear to reflect a crossover behaviour to an exponent beta'=0 at zero disorder strength. The conclusions of this paper strongly rely on analytical arguments. A scaling theory in terms of the disorder strength and the magnetic field is presented that gives the values of all critical exponent except for one, the value of which is estimated from scaling arguments.

cond-mat.dis-nn↗

arXiv1997

Dynamics of a single particle in a horizontally shaken box

We study the dynamics of a particle in a horizontally and periodically shaken box as a function of the box parameters and the coefficient of restitution. For certain parameter values, the particle becomes regularly chattered at one of the walls, thereby loosing all its kinetic energy relative to that wall. The number of container oscillations between two chattering events depends in a fractal manner on the parameters of the system. In contrast to a vertically vibrated particle, for which chattering is claimed to be the generic fate, the horizontally shaken particle can become trapped on a periodic orbit and follow the period-doubling route to chaos when the coefficient of restitution is changed. We also discuss the case of a completely elastic particle, and the influence of friction between the particle and the bottom of the container.

chao-dyn↗

arXiv1997

Phase Transitions in a Nonequilibrium Percolation Model

We investigate the percolation properties of a two-state (occupied - empty) cellular automaton, where at each time step a cluster of occupied sites is removed and the same number of randomly chosen empty sites are occupied again. We find a finite region of critical behavior, formation of synchronized stripes, additional phase transitions, as well as violation of the usual finite-size scaling and hyperscaling relations, phenomena that are very different from conventional percolation systems. We explain the mechanisms behind all these phenomena using computer simulations and analytic arguments.

cond-mat.stat-mech↗

arXiv1997

Winding angles for two-dimensional polymers with orientation dependent interactions

We study winding angles of oriented polymers with orientation-dependent interaction in two dimensions. Using exact analytical calculations, computer simulations, and phenomenological arguments, we succeed in finding the variance of the winding angle for most of the phase diagram. Our results suggest that the winding angle distribution is a universal quantity, and that the $θ$--point is the point where the three phase boundaries between the swollen, the normal collapsed, and the spiral collapsed phase meet. The transition between the normal collapsed phase and the spiral phase is shown to be continuous.

cond-mat.stat-mech↗

arXiv1996

Forest fires and other examples of self-organized criticality

We review the properties of the self-organized critical (SOC) forest-fire model. The paradigm of self-organized criticality refers to the tendency of certain large dissipative systems to drive themselves into a critical state independent of the initial conditions and without fine-tuning of the parameters. After an introduction, we define the rules of the model and discuss various large-scale structures which may appear in this system. The origin of the critical behavior is explained, critical exponents are introduced, and scaling relations between the exponents are derived. Results of computer simulations and analytical calculations are summarized. The existence of an upper critical dimension and the universality of the critical behavior under changes of lattice symmetry or the introduction of immunity are discussed. A survey of interesting modifications of the forest-fire model is given. Finally, several other important SOC models are briefly described.

cond-mat.stat-mech↗

arXiv1996

Self--organized criticality due to a separation of energy scales

Certain systems with slow driving and avalanche-like dissipation events are naturally close to a critical point when the ratio of two energy scales is large. The first energy scale is the threshold above which an avalanche is triggered, the second scale is the threshold above which a site is affected by an avalanche. I present results of computer simulations, and a mean-field theory.

cond-mat.stat-mech↗

arXiv1996

Winding Angle Distributions for Directed Polymers

We study analytically and numerically the winding of directed polymers of length $t$ around each other or around a rod. Unconfined polymers in pure media have exponentially decaying winding angle distributions, the decay constant depending on whether the interaction is repulsive or neutral, but not on microscopic details. In the presence of a chiral asymmetry, the exponential tails become non universal. In all these cases the mean winding angle is proportional to $\ln t$. When the polymer is confined to a finite region around the winding center, e.g. due to an attractive interaction, the winding angle distribution is Gaussian, with a variance proportional to $t$. We also examine the windings of polymers in random systems. Our results suggest that randomness reduces entanglements, leading to a narrow (Gaussian) distribution with a mean winding angle of the order of $\sqrt{\ln t}$.

cond-mat.stat-mech↗

arXiv1996

Interface roughening with nonlinear surface tension

Using stability arguments, this Brief Report suggests that a term that enhances the surface tension in the presence of large height fluctuations should be included in the Kardar-Parisi-Zhang equation. A one-loop renormalization group analysis then shows for interface dimensions larger than $\simeq 3.3$ an unstable strong-coupling fixed point that enters the system from infinity. The relevance of these results to the roughening transition is discussed.

cond-mat.stat-mech↗